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Atlas › Integer Profiles › Node 27,100,736

27,100,736

26 × 13 × 32573
Abundant Even Composite

27,100,736 factors as 2^6 × 13 × 32573. Its 28 positive divisors give a proper-divisor sum of 30,815,836, so this integer is abundant. The Collatz stopping time is 87 steps.

Prime Factor Structure

Factorization String 2^6 × 13 × 32573
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 57,916,572
Proper Divisor Sum 30,815,836
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #27100709 ← → #27100741

Radix Representation

Decimal 27100736
Binary 1100111011000011001000000 (25 bits)
Octal 0o147303100
Hexadecimal 0x19D8640

Divisor Catalog (28)

1 2 4 8 13 16 26 32 52 64 104 208 416 832 32,573 65,146 130,292 260,584 423,449 521,168 846,898 1,042,336 1,693,796 2,084,672 3,387,592 6,775,184 13,550,368 27,100,736

Collatz Trajectory (87 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

27,100,736 13,550,368 6,775,184 3,387,592 1,693,796 846,898 423,449 1,270,348 635,174 317,587 952,762 476,381 1,429,144 714,572 357,286 178,643 535,930 267,965 803,896 401,948 200,974 100,487 301,462 150,731 452,194 226,097 678,292 339,146 169,573 508,720 254,360 127,180 63,590 31,795 95,386 47,693 143,080 71,540 35,770 17,885 53,656 26,828 13,414 6,707 20,122 10,061 30,184 15,092 7,546 3,773 11,320 5,660 2,830 1,415 4,246 2,123 6,370 3,185 9,556 4,778

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